# Atomic Physics 2018

For each poster contribution there will be one poster wall available (A0 size). Posters can be put up for the full duration of the workshop.

### Stable single light bullets in cold Rydberg gases

Bai, Zhengyang

Realizing single light bullets and vortices that are stable in high dimensions is a long-standing goal in the study of nonlinear optical physics. On the other hand, the storage and retrieval of such stable high dimensional optical pulses may offer a variety of applications. Here we present a scheme to generate such optical pulses in a cold Rydberg atomic gas. By virtue of electromagnetically induced transparency, strong, long-range atom-atom interaction in Rydberg states is mapped to light fields, resulting in a giant, fast-responding nonlocal Kerr nonlinearity and the formation of light bullets and vortices carrying orbital angular momenta, which have extremely low generation power, very slow propagation velocity, and can stably propagate, with the stability provided by the combination of local and the nonlocal Kerr nonlinearities. We demonstrate that the light bullets and vortices obtained can be stored and retrieved in the system with high efficiency and fidelity. Our study provides a new route for manipulating high-dimensional nonlinear optical processes via the controlled optical nonlinearities in cold Rydberg gases.

### Electron dynamics in twisted light modes of relativistic intensity

Baumann, Christoph

In the past two decades, twisted light beams have been extensively studied according to their unique properties. A Laguerre-Gaussian (LG) laser beam, for instance, describes such a twisted mode that can be obtained as a higher-order solution to the paraxial wave equation. In contrast to common laser beams, these twisted beams are characterized by their well-defined orbital angular momentum (OAM). As a result, they can enable completely new insights into the dynamics of a physical system, thus leading to a wide range of applications in quantum information, spectroscopy, etc. It is therefore important to understand in detail how particles behave in such field configurations. The present work addresses this question by studying the interaction of electrons with different circularly-polarized LG modes in the relativistic intensity regime. Three-dimensional particle-in-cell simulations indicate that the electron dynamics are not only very sensitive to the LG mode parameters, but also to the helicity s of the laser radiation. In particular, the present contribution will report on the generation of twisted electron beams. It turns out that the number of twisted electron beams cannot adopt an arbitrary value. Instead, the number is fully determined by the angular momentum of the LG mode m and the helicity of the laser s. Beyond this quantization, these beams are additionally characterized by durations of the order of hundreds of attoseconds [1]. [1] C. Baumann and A. Pukhov, Phys. Plasmas 25, 083114 (2018)

### “Coherent transitions” and Rabi-type oscillations between modes of classical light in fiber-like structures

Bogatskaya, Anna

We apply approaches and concepts from quantum mechanics to the classical problem of light beam propagation in the elements of integrated optical circuits. We consider here fiber-like structures in opaque media as potential wells between complex-shaped barriers. This allowed us to construct an analogy between coherent oscillations in a quantum system and the redistribution in space of the field strength of a classical wave in the framework of the slow-varying amplitude approximation for the wave equation. We have demonstrated capability to control the mode composition of a classical light in a fiber-like structure with heterogeneous boundaries. The proposed description for the field spatial redistribution was based on the analogy with Rabi-type oscillations in quantum mechanics. The fundamental analogy between optics and quantum mechanics was recently used by us in order to analyze an important applied problem of radio communication blackout during the spacecraft reentry [1]. [1] Anna Bogatskaya, Nikolay Klenov, Maxim Tereshonok, Sergey Adjemov, and Alexander Popov, J. Phys. D: Appl. Phys. 51, 185602 (2018)

### Differential cross sections for single ionization of Li by protons and O8+ ions

Bondarev, Andrey

COLTRIMS (cold target recoil-ion momentum spectroscopy) or reaction microscope technique [1,2] provides a way to measure fully differential cross sections for ionization in ion-atom collisions. Such cross sections contain complete information on ionization dynamics and serve as unique tests of theory. Successful implementation of the MOTReMi (magneto-optical trap reaction microscope) technique [3] extends the range of possible targets for kinematically complete experiments from atomic helium and molecular hydrogen to lithium atom. Moreover, in MOTReMi a target can be prepared in an excited state and at lower temperature. The latter results in better momentum resolution of measurements. Up to now, differential cross sections for single ionization of lithium atom in collisions with various projectiles were measured in a number of experiments [4,5,6]. Recently a semiclassical non-perturbative method based on the Dirac equation for calculation of differential cross sections for ionization in ion-atom collisions was developed. The method was described in detail in Ref. [7] and applied to antiproton-impact ionization of atomic hydrogen. In this report, we present results of differential ionization cross section calculation in collisions of protons and bare oxygen nuclei with lithium atom. The obtained results are compared with experimental data and available theoretical predictions. __________ [1] R. Dörner et al., Phys. Rep. 330, 95 (2000). [2] J. Ullrich et al., Rep. Prog. Phys. 66, 1463 (2003). [3] R. Hubele et al., Rev. Sci. Instrum. 86, 033105 (2015). [4] A. C. LaForge et al., J. Phys. B 46, 031001 (2013). [5] R. Hubele et al., Phys. Rev. Lett. 110, 133201 (2013). [6] E. Ghanbari-Adivi et al., J. Phys. B 50, 215202 (2017). [7] A. I. Bondarev et al., Phys. Rev. A 95, 052709 (2017).

### Comparative study of single and double ionization dynamics from single and double excitations in helium

Borisova, Gergana D.

The helium atom has established itself as an exemplary system to study two-electron effects both theoretically and experimentally. Here, we present theoretical results from our study of the two-electron dynamics in a helium atom interacting with strong laser fields. We employ a numerical quantum-mechanical model based on solving the one-dimensional time-dependent Schrödinger equation for two electrons, where the ionization dynamics of the excited states are the main focus of this work. The theoretical method ensures direct access to the time-dependent population of the relevant atomic states during and right after the interaction with the near-infrared (NIR) laser pulse. A partition technique applied to the wave function grid is used for the quantitative study of strong-field ionization dynamics of the initially prepared bound excited states. We find that both the singly excited states (SES) and the doubly excited states (DES) predominantly ionize in the process of single ionization. In the DES however, the second electron can be driven out of its bound state orbital, leading to an enhanced double ionization yield.

### High-order above treshold ionization beyond the electric dipole approximation

Brennecke, Simon

Laser-induced electron diffraction (LIED) is a tool for imaging atomic and molecular structural changes with subangstrom spatial and few-femtosecond temporal resolutions. This technique is based on recolliding electrons in linearly polarized laser pulses leading to high-order above-threshold ionization (HATI) and its interpretation is usually carried out in electric-dipole approximation. Here, we present a detailed analysis of effects beyond the electric-dipole approximation in the HATI region. To this end, photoelectron momentum distributions from strong-field ionization are calculated by numerical solution of the one-electron time-dependent Schrödinger equation for model atoms and small molecules including leading order non-dipole effects. For high-energy electrons from rescattering we observe the following two major deviations from the dipole approximation: (i) The minima and maxima resulting from interference between short and long rescattering trajectories are shifted along the field propagation direction; (ii) an asymmetry in the signal strength of electrons emitted in the forward/backward directions appears. Taken together, the two non-dipole effects give rise to a considerable average forward momentum component of the order of 0.1 a.u. for realistic laser parameters. We develop a non-dipole classical three-step model including the beyond-dipole Lorentz force and incorporating accurate quantum-mechanical cross sections to interpret the shift of the boundary and also the asymmetry in the outer part of the distribution. Additionally, a non-dipole quantum-orbit model provides the foundation for a quantitative understanding of the complete HATI region at least for short-range potentials and offers a transparent interpretation of the underlying physics.

### Different time scales in plasmonically enhanced high-order harmonic generation

Chomet, Heloise

We investigate high-order harmonic generation in inhomogeneous media for reduced dimensionality models. We perform a phase-space analysis, in which we identify specific features caused by the field inhomogeneity. We compute high-order harmonic spectra using the numerical solution of the time-dependent Schrodinger equation, and provide an interpretation in terms of classical electron trajectories. We show that the dynamics of the system can be described by the interplay of high-frequency and slow-frequency oscillations, which are given by Mathieu’s equations. The latter oscillations lead to an increase in the cutoff energy, and, for small values of the inhomogeneity parameter, take place over many driving-field cycles. In this case, the two processes can be decoupled and the oscillations can be described analytically.

### Influence of topological edge states on the harmonic generation in linear chains

Drüeke, Helena

The two topological phases of a linear chain of ions differ in their harmonic yields by several orders of magnitude due to the difference in the destructive interference of all valence band and edge state electrons. A program to solve the time-dependent Kohn-Sham equations has been developed. It allows for the simulation of a linear chain in an intense laser field in an all-electron, self-consistent way. The robustness of the differing harmonic yield was investigated with respect to finite-size and disorder effects. A remarkable robustness was observed, which might allow applications that steer topological electronics by all-optical means or control strong-field-based light sources electronically.

### High Harmonics generation from excited states of atoms

Efimov, Dmitry

We study High Harmonics spectra generated by atoms during their interaction with strong short laser field. We show that initial excitation of atom essentially moderates the shape of HHG spectrum.

### Classical features in high-order above-threshold ionization of molecular hydrogen cation: ab initio vs classical trajectory method

Fetić, Benjamin

B. Feti\'{c}$^1$ and D. B. Milo\v{s}evi\'{c}$^{1,2}$ 1Faculty of Science, University of Sarajevo, Zmaja od Bosne 35, 71000 Sarajevo, Bosnia and Herzegovina 2Academy of Sciences and Arts of Bosnia and Herzegovina, Bistrik 7, 71000 Sarajevo, Bosnia and Herzegovina Corresponding author: benjamin.fetic@gmail.com In the last two decades classical trajectory approach has played a crucial role in understanding the basic physical mechanism of high-order above-threshold ionization (HATI) (for a historical review and more see [1]). This approach has become to be known as Simple man's theory or three-step model [2] and is well understood for atomic targets. According to this model for atomic targets, an atom is ionized and, at some instant of time, the liberated electron is driven back to the parent ion at which it elastically scatters in arbitrary direction. In the case of diatomic molecular targets, an electron can be liberated from any of the atomic centers, so that it can be “born” in the vicinity of one or the other atomic center. Therefore, we expect some novel features in the molecular HATI spectra in comparison to the atomic HATI. In this work we will explore some of these features obtained using numerical solution of the 3D time-dependent Schrödinger equation [3] and solutions of the Newton's equation of motion for electron in linearly polarized laser field. References: [1] W. Becker, S. P. Goreslavski, D. B. Milošević and G. G. Paulus, J. Phys. B: At. Mol. Opt. Phys. 51, 162002 (2018). [2] P. B. Corkum, Phys. Rev. Lett. 71, 1994 (1993), for HHG, and: G. G. Paulus, W. Becker, W. Nicklich, and H. Walther, J. Phys. B 27, L703 (1994), for HATI. [3] B. Fetić and D. B. Milošević, Phys. Rev. E 95, 053309 (2017).

### Coupled Coherent States for Indistinguishable Bosons

Green, James

The coupled coherent states (CCS) trajectory guided Gaussian method of multidimensional quantum dynamics has been well established as a theoretical technique used to treat systems of distinguishable particles. In this present work we look at extending the CCS formalism to treat systems of indistinguishable bosons (CCSB) via second quantisation. The relevant working equations of CCSB are presented, alongside application to two model problems. The first is a system-bath problem consisting of a tunnelling mode coupled to a harmonic bath, previously studied by CCS and other methods in distinguishable representation in 20 dimensions. The harmonic bath is comprised of identical oscillators, and may be second quantised for use with CCSB. The cross-correlation function for the dynamics of the system and Fourier transform spectrum compare extremely well with a benchmark calculation. The second model problem involves 100 bosons in a shifted harmonic trap. Oscillations in the 1-body density are calculated and shown to compare favourably to a multiconfigurational time-dependent Hartree for bosons calculation.

### Complex Scaling in Non-Hermitian 2-level Hamiltonian

Hofmann, Cornelia

We numerically model a two-level system of helium with the ground state and an autoionizing excited state. It has been suggested to model this two-level Hamiltonian in a complex scaled form [1], where both the life time of the excited state as well as the action of a coupling laser pulse is treated in complex values. This system exhibits an exceptional point, such that for specific field amplitude and carrier frequency the two states coalesce in the Floquet picture. We numerically solve the corresponding time-dependent Schröndiger equation and study the dynamic evolution of the wave packet populations in both states. The results indicate that the dynamics of the system are qualitatively the same, independent of whether the complex scaling of the laser coupling is applied or not. [1] Kaprálová-Žďánská, P. R., & Moiseyev, N. (2014). Helium in chirped laser fields as a time-asymmetric atomic switch. The Journal of Chemical Physics, 141(1), 014307. https://doi.org/10.1063/1.4885136

### Scaling relations of the time-dependent Dirac equation describing multiphoton ionization

Ivanova, Irina

Approximate scaling laws with respect to the nuclear charge are introduced for the time-dependent Dirac equation describing hydrogen-like ions subject to laser fields within the dipole approximation. In particular, scaling relations with respect to the laser wavelengths and peak intensities are discussed. The validity of the scaling relations is investigated for two-, three-, four-, and five-photon ionization of hydrogen-like ions with the nuclear charges ranging from Z=1 to 92 by solving the corresponding time-dependent Dirac equations adopting the properly scaled laser parameters. Good agreement is found and thus the approximate scaling relations are shown to capture the dominant effect of the response of highly-charged ions to intense laser fields compared to the one of atomic hydrogen. On the other hand, the remaining differences are shown to allow for the identification and quantification of additional, purely relativistic effects in light-matter interaction.

### Pseudopotential of Many-Electron Atoms

Jobunga, Eric Ouma

Atoms form the basic building blocks of molecules and condensed matter. Other than hydrogen atom, all the others have more than one electron which interact with each other besides interacting with the nucleus. Electron-electron correlation forms the basis of difficulties encountered in many-body problems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in the correlation. In an effort to tackle this many-body problem, two complementary parameter-free pseudopotentials for $n$-electron atoms and ions are suggested in this study. Using one of the pseudopotentials, near-exact values of the groundstate ionization potentials of helium, lithium, and berrylium atoms have been calculated. The other pseudopotential also proves to be capable of yielding reasonable and reliable quantum physical observables within the non-relativistic quantum mechanics.

### High-Harmonic Generation in a Su-Schrieffer-Heeger Chain

Jürß, Christoph

High-harmonic spectra for two topological phases of a one-dimensional, linear chain were investigated previously using time dependent density functional theory [1]. A significant difference in the dipole strength between the two topological phases were observed and explained by destructive interferences of emitted light from the electrons in the valence-band. We obtain similar results as we couple the tight-binding based Su-Schrieffer-Heeger model to an external field. Edge states and spectra in this model are quite robust against random fluctuations of the system. Additionally the bulk-surface correspondence is investigated by focusing the laser to certain areas of the chain. [1] D. Bauer, K. K. Hansen, Phys. Rev. Lett. 120, 177401 (2018)

### Non-adiabatic quantum trajectories in Strong Field Ionisation

Kaushal, Jivesh

The initial conditions for electron trajectories at the exit from the tunnelling barrier are often used in strong field models, for example to bridge the first and second steps of the well-known 3-step model. Our Analytical R-Matrix (ARM) theory does not rely on the 3-step model or the concept of the tunnelling barrier in coordinate space. Defining initial conditions for electron trajectories at the barrier exit is, strictly speaking, not necessary to calculate standard observables in this formalism. Not necessary, but possible. The opportunity to evaluate such initial conditions emerges as a corollary of analysing sub-barrier kinematics, which includes the interplay of laser and Coulomb fields on the sub-cycle scale. We apply our results to discuss the difference in such initial conditions for co- and counter-rotating electrons liberated during strong field ionisation. We also study their impact on subsequent non-adiabatic quantum trajectories emerging for different electron orientations in the atom.

### Derivation of the quantum-mechanical kinetic energy operator for triatomic molecules with coordinate-dependent nuclear masses

Khoma, Mykhaylo

The aim of our study is to derive an effective kinetic energy operator (KEO) for a triatomic system which accounts for nonadiabatic effects represented by introducing coordinate-dependent reduced nuclear masses. The purpose of such operator is to simulate a full $N$-body level of theory but staying in the paradigm of the adiabatic theory (i.e. utilizing the concept of adiabatic potential energy surfaces). The derivation has been carried out in the spirit of the work of Herman and Asgharian [1], resulting in effective vibrational and rotational coordinate-dependent contributions to the reduced nuclear mass of the diatomic system. For a triatomic system we start from the \emph{ad-hoc} Cartesian KEO in the body-fixed (BF) frame $$\label{T3D-ini} T_{Cart} = -\frac{\hbar^2}{2} \sum_{\alpha=x,y,z} \frac{1}{\mu_{r}^{(\alpha)}} \frac{\partial^2}{\partial {\alpha}^2} -\frac{\hbar^2}{2} \sum_{\alpha=X,Y,Z} \frac{1}{\mu_{R}^{(\alpha)}} \frac{\partial^2}{\partial {\alpha}^2},$$ where $\vec{r}(x,y,z)$ and $\vec{R}(X,Y,Z)$ are the Jacobi coordinate vectors. Our task is to transform the $T_{Cart}$ into an expression $T_{mol}$ in generalized (non-orthogonal) molecular coordinates in arbitrarily oriented space-fixed (SF) frame. The main difficulties in the construction of the $T_{mol}$ in SF frame are related to a presence of the different mass-prefactors (reduced masses) ${\mu_{r}^{(x,y,z)}}$ and ${\mu_{R}^{(X,Y,Z)}}$ in the expression $T_{Cart}$. We have proposed a new scheme for the derivation of the $T_{mol}$ based on the chain rule method with a usage of infinitesimal variations of the generalized coordinates [2]. Within this method, the triatomic KEO $T_{mol}=K_V + K_{VR}$ has been derived, where $K_V$ and $K_{VR}$ are the vibrational and rovibrational parts of the total KEO. It was found that $K_{VR}$ (and therefore $T_{mol}$) preserves the total rotational invariance with respect to the Euler rotations. This allows constructing a compact representation for an effective nonadiabatic Hamiltonian for triatomic molecules [3]. Preliminary applications for the rovibrational spectrum of H$_3^+$ have been already performed [4]. \vspace{5mm} \small \noindent [1] R. M. Herman, A. Asgharian, \emph{J. Mol. Spectr.} {\bf 19} {305} (1966) \noindent [2] M. Khoma, R. Jaquet, \emph{J. Chem. Phys}. {\bf 147} 114106 (2017) \noindent [3] M. Khoma, R. Jaquet, \emph{J. Math. Chem.} (submitted) \noindent [4] R. Jaquet, M. Khoma, \emph{J. Phys. Chem. A} {\bf 121} 7016 (2017); R. Jaquet, M. Khoma, \emph{Mol. Phys.} {\bf 116} {3507} (2018)

### Scaling Laws for a Hydrogen-like Ion in an Intense Laser Field

Khujakulov, Anvar

We study hydrogen-like ions interacting with intense ultra-short laser pulses. Within the dipole approximation the time-dependent Schr\"{o}dinger equation (TDSE) of hydrogen-like ions can be mapped onto the one of the hydrogen by scaling properly [L. B. Madsen and P. Lambropoulos Phys.\,Rev.\,A \textbf{59}, 4574 (1999)]. Relativistic effects must be taken into account if hydrogen-like ions with increasing nuclear charges are considered. In contrast to the non-relativistic regime, strict analytic scaling relations are not known for the Dirac equation. The validity of the non-relativistic scaling relations applied to the solution of the Dirac equation is investigated in the quasi-static regime. For this purpose, the time-independent Schr\""{o}dinger and Dirac equations are solved for hydrogen-like ions in a static electric field using the complex-scaling method. Possible improvements of the scaling relations are discussed. "

### Strong field physics in the Coulomb system using complex classical trajectories

Koch, Werner

Complex-valued semiclassical methods hold out the promise of providing insight into the physical nature of a dynamical system while treating classically allowed and classically forbidden processes on the same footing. Their fundamental elegance notwithstanding, these methods have been severely hampered by the numerical and conceptual difficulties introduced by the complexification. Recent progress in the understanding of the topology of complex space and complex time eliminates these problems allowing for stable, long time wave packet reconstruction from the complex trajectory manifolds. We apply this approach to the laser driven dynamics of the ground state of the Coulomb system and present wave functions and spectra in good agreement with numerical quantum results. Individual ionization and recollision processes can be identified and their contributions to the final results can be studied independently or in combination.

### Manifesting Berry phase in graphene without magnetic field

Koochakikelardeh, Hamed

We theoretically explore the electron dynamics of graphene superlattices created by strong circularly-polarized ultrashort pulses. The conduction-band population distribution in the reciprocal space forms an interferogram with discontinuities related to the topological (Berry) ﬂuxes at the Dirac points. One of the fundamental problems of topological physics of graphene is a direct observation of the Berry phase. This is related to the fact that the only realistic possibility of observing this phase is self-referenced interferometry of electronic waves in the reciprocal space. However, the Berry phase is ±π; the self-referenced interferometry doubles it to ±2π, which does not produce any discontinuities in the interference fringes. The Bragg scattering from the superlattices creates diffraction and “which way” interference in the reciprocal space reducing the Berry phase and making it directly observable in the electron interferograms. Our finding is an essential step in control and observation of ultrafast electron dynamics in topological solids and may open up a route to all-optical switching, ultrafast memories, and room temperature superconductivity technologies.

### Ground-State Energy of Heavy Diatomic Homonuclear Quasimolecules

Kotov, Artem

Few-electron diatomic quasimolecules represent the simplest molecular systems. One of the most interesting cases is heavy quasimolecules in which $Z > 173$ ($Z = Z_1 + Z_2$ is the total nuclear charge). The electromagnetic field strength in such systems can be high enough to approach the critical field strength in the Schwinger mechanism $E_{c}=m^2c^3 / (\hbar e)\simeq 1.3\cdot 10^{16} \, \text{V}/\text{cm}$, i.e. spontaneous electron-positron pair production becomes possible [1]. In other words, the lowest-lying electronic state is close to dive'' into the Dirac negative-energy continuum at small enough internuclear distances [2]. In this case the parameter $\alpha Z$ is not small ($\alpha$ is the fine-structure constant) so calculations should be done to all orders in $\alpha Z$. We present relativistic calculations of the ground-state energy of one- and two-electron diatomic uranium quasimolecule valid to all orders in $\alpha Z$. The Dirac equation with the two-center potential is solved numerically using the dual-kinetic-balance method [3]. The self-energy and vacuum-polarization corrections are calculated in the monopole approximation. The results obtained are compared with the results of the previous calculations [4-7]. For two-electron heavy quasimolecules we evaluate also the electron-electron interaction effects. The one-photon exchange is calculated for the two-center potential and the two-photon exchange --- in the monopole approximation of the potential. The higher-order corrections are calculated within the Breit approximation. To the best of our knowledge, this is the most accurate up-to-date evaluation of the two-electron quasimolecular binding energies. ----- [1] Y. B. Zeldovich and V. S. Popov, Sov. Phys. Usp. 14, 673 (1972). [2] W. Greiner, B. Müller, and J. Rafelski, Quantum electrodynamics of strong fields (Springer- Verlag, Berlin, 1985). [3] E. D. Rozenbaum, D. A. Glazov, V. M. Shabaev, K. E. Sosnova, and D. A. Telnov, Phys. Rev. A 89, 012514 (2014). [4] I. I. Tupitsyn and D. V. Mironova, Opt. Spectrosc. 117, 351 (2014). [5] D. V. Mironova, I. I. Tupitsyn, V. M. Shabaev, and G. Plunien, Chem. Phys. 449, 10 (2015). [6] A. N. Artemyev and A. Surzhykov, Phys. Rev. Lett. 114, 243004 (2015). [7] A. Roenko and K. Sveshnikov, Phys. Rev. A 97, 012113 (2018).

### Quantum Dynamics on a Torus

Kraus, Michael

The trajectory of a classical particle confined to a torus can be mapped onto the dynamics of two independent oscillators. Periodic closed orbits occur when the frequencies of these two oscillators are commensurable, otherwise the motion is quasiperiodic. We explored the quantum/classical behavior of this system utilizing the method of Bohm trajectories, and studied the influence of the type of classical behavior on the observables that are determined quantum mechanically.

### Learning ionization control landscape using artificial neural network

Kumar Giri, Sajal

### Bright terahertz-radiation source from two-color mid-infrared laser interacting with a microplasma target

Liseykina, Tatyana

A way of a considerable enhancement of the terahertz (THz) radiation from atomic gases, irradiated by an intense mid-infrared laser light has been recently suggested (\textit{V. A. Tulsky, M. Baghery, U. Saalmann, S. V. Popruzhenko, arXiv:1810.08834v1}). In particular, theoretical analysis of both the single-atom-ionization dynamics and the collective motion of the laser-generated plasma (restricted to the 1D model) confirmed that the application of the circularly polarized laser light with 2-4 micrometer wavelength may result in considerable increase of the conversion efficiency of the infrared radiation into the emitted THz waves. In this work the results of the 2D particle-in-cell modeling of the THz response in the case of a two-color mid-infrared laser pulse propagating in argon will be presented.

### High-harmonic spectroscopy of Floquet-Bloch bands

Medisauskas, Lukas

High harmonic generation (HHG) in solid state materials is know to be largely determined by the band structure. However, a strong electromagnetic field not only drives the electronic dynamics, but also modifies the underlying electronic states via the AC Stark effect. In solids, this can lead to the formation of Floquet-Bloch bands, which can have properties that are very different from their field-free counterparts. We investigate such laser-dressed'' bands in a model dielectric exposed to a strong and low frequency field such as used in HHG experiments. By solving the time-dependent Schroedinger equation and using an expansion into photon-number states, we reveal the underlying field-dressed bands. Furthermore, we show that they lead to harmonics that follow field-dressed band-gap as pulse intensity changes.

### Modelling of self-sustained QED cascades in slow varying electromagnetic field

Mironov, Arseniy

QED cascades are chains of consequent non-linear processes of photon emission by ultra-relativistic electrons and $e^-e^+$ pair photoproduction in presence of some electromagnetic field. Self-sustained QED cascades driven by external field are one of the brightest intense-field QED effects that might be observed at the new laser facilities once ultra-high intensities of order of $10^{23}$--$10^{24}$ W/cm$^2$ will be available. Modern techniques for simulation of QED cascades rely on semi-classical approach. It implies that particles propagate along classical trajectories, while quantum events of emission and photoproduction occur spontaneously and are localized. Taking this as a basis we develop a qualitative theory for the initial stage of cascade formation for a general class of slow varying electromagnetic fields of electric type ($E^2-H^2>0$). We will discuss some aspects of our theory and cascade simulations. For instance, our theory allows to derive general condition of QED cascade initiation. The research was supported by the MEPhI Academic Excellence Project and the Russian Fund for Basic Research (Grant No. 16-02-00963a).

### Shape transition in two-electron quantum dots in a magnetic field

Nazmitdinov, Rashid

We found that the interplay of the classical and quantum properties of two-electron quantum dots lead to a quantum shape transition from a lateral to a vertical localization of electrons in low-lying excited states at relatively strong Coulomb interaction with alteration of the magnetic field. In contrast, in that regime in the ground states the electrons form always a ring type distribution in the lateral plane.

### Generalized perspective on chiral measurements without magnetic interactions

Ordonez, Andres

We present a unified description of several methods of chiral discrimination based exclusively on electric-dipole interactions. It includes photoelectron circular dichroism (PECD), enantio-sensitive microwave spectroscopy (EMWS), photoexcitation circular dichroism (PXCD) and photoelectron-photoexcitation circular dichroism (PXECD). We show that, in spite of the fact that the physics underlying the appearance of a chiral response is very different in all these methods, the enantio-sensitive and dichroic observable in all cases has a unique form. It is a polar vector given by the product of (i) a molecular pseudoscalar and (ii) a field pseudovector specified by the configuration of the electric fields interacting with the isotropic ensemble of chiral molecules. The molecular pseudoscalar is a rotationally invariant property, which is composed from different molecule-specific vectors and in the simplest case is a triple product of such vectors. The key property that enables the chiral response is the non-coplanarity of the vectors forming such triple product. The key prop- erty that enables chiral detection without relying on the chirality of the electromagnetic fields is the vectorial nature of the dichroic and enantio-sensitive observable. Our compact and general expression for this observable shows what ultimately determines the efficiency of the chiral signal. We extend these methods to arbitrary polarizations of the electric fields used to induce and probe the chiral response. arXiv:1802.06540

### New Approach to Generation and Amplification of the THz Radiation in Plasma Created by Intense Two-Color Laser Fields

Popov, Alexander

New approach to the problem of generation and amplification of electromagnetic radiation of the terahertz frequency band in strongly nonequilibrium plasma channels created by high-intensity laser radiation in gases is discussed. This approach is based on the two-color laser induced THz background production in different nonlinear processes during the pulse of in the after-pulse regime and its further amplification in the plasma channel with population inversion formed by the laser pulse. Special attention is paid to the case of nearly-resonant background formation in aluminum vapor irradiated by Ti-Sa laser pulse and its second harmonic.

### Semiclassical description of HHG in H$_2^+$

Rodríguez-Hernández, Fermín

### Going beyond the perturbative regime: Post-Marcus methods based on the Generalized Quantum Master Equation

Schubert, Alexander

We present a modified approach for simulating electronically nonadiabatic dynamics based on the Nakajima-Zwanzig generalized quantum master equation (GQME). The key feature of the modified approach over previously proposed GQME-based approaches is that it benefits from the fact that the Nakajima-Zwanzig formalism does not require casting the overall Hamiltonian in system-bath form, which is arguably neither natural nor convenient in the case of the Hamiltonian that governs nonadiabatic dynamics. Within the modified approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density operator is fully captured by a memory kernel super-operator. A methodology for calculating the memory kernel from projection-free inputs is developed. Simulating the electronic dynamics via the modified approach, with a memory kernel obtained using exact or approximate methods, can be more cost effective and/or lead to more accurate results than direct application of those methods. The modified approach is demonstrated on a benchmark spin-boson model with a memory kernel which is calculated within the Ehrenfest mean-field method.

### Extension of the strong-field approximation to describe simultaneous double ionization of $\text{C}_{\text{60}}$

Schubert, Ingmar

A formalism to extend the strong-field approximation (SFA) to large molecular systems is presented. Using this formalism, the single-electron ionization yields for a rigid-rotor model of fullerene ($\text{C}_{\text{60}}$) in a half-cycle pulse are calculated and compared to the full numerical solution of the time-dependent Schrödinger equation within the single-active-electron approximation. This newly extended SFA is then used to calculate the yields for simultaneous two-electron ionization of $\text{C}_{\text{60}}$.

### CEP dependence of the enhanced ionization of HeH$^+$ driven by intense ultrashort laser pulses

Schulz, Bruno

We study the electronic motion of the enhanced ionization of $HeH^+$ by solving the six-dimensional time-dependent Schroedinger equation within the fixed nuclei approximation. We demonstrate that the electronic motion is much richer than indicated by the laser pulse which is a direct consequence of the Stark-shifted energies. Moreover, we show that there is a huge carrier-envelope phase effect due to the asymmetry of the Stark-shift for a short laser pulse. This manifests in an almost vanishing population of the first excited state at R=3.7 for CEP zero, while the for the CEP $\pi$ case the population of the excited state is 60 %. Due to this relatively simple change of the CEP the electronic motion is completely different.

### Further developments of semiclassical two-step model: Multielectron polarization effects and ionization of hydrogen molecule

Shvetsov-Shilovskiy, Nikolay

We extend the semiclassical two-step model to include a multielectron polarization-induced dipole potential. We investigate the imprints of multielectron effects in the momentum distributions of photoelectrons ionized by a linearly polarized laser pulse. We predict narrowing of the longitudinal momentum distributions due to electron focusing by the induced dipole potential. The polarization of the core also modifies interference structures in the photoelectron momentum distributions. Specifically, the number of fanlike interference structures in the low-energy part of the electron momentum distribution may be altered. We analyze the mechanisms underlying these effects. The account of the multielectron dipole potential seems to improve the agreement between theory and experiment. Furthermore, we extend the semiclassical two-step model to the hydrogen molecule. In the simplest case of the molecule oriented along the polarization direction of a linearly polarized laser field, we predict significant deviations of the photoelectron momentum distributions and the energy spectra from the case of atomic hydrogen. For the hydrogen molecule the energy spectrum falls off slower with increasing energy, and the holographic interference fringes are more pronounced than for the hydrogen atom at the same parameters of the laser pulse.

### Phase-dependent photoemission from Xenon and C60 molecule investigated by the „phase-of-the-phase spectroscopy”

Skruszewicz, Slawomir

Strong field ionization of atomic and molecular systems with tailored laser fields provides insight into the ionization and electron rescattering dynamics in atomic and molecular systems. We investigate the ionization and rescattering dynamics in Xenon and $C_{60}$ molecule with sw-IR wavelengths by applying recently introduced the “phase-of-the-phase” (PoP) spectroscopy [1,2]. PoP quantifies the amplitude and the phase lag of the electron yield changes as a function of the relative phase of the

### Reconstructing real-time quantum dynamics in strong and short laser fields

Stooß, Veit

In light-matter interaction, information about the dynamics of the matter part is encoded in the ultrafast, time-dependent, motion of the electron distribution, in other words, the electronic response. We present a method which allows the retrieval of the entire holographic (amplitude and phase) time-resolved information about the state specific electronic response of bound electron systems by recording the transient absorption spectrum of just one single ultrashort probe signal [1]. Most importantly, this still holds for the case of coherently excited systems interacting with multiple laser pulses, which therefore may exhibit non-trivial time dependence due to the interaction with strong external fields. Our finding is applied to the time-domain observation of excited-state dynamics of a two-electron system during the interaction with a strong laser pulse in the few-femtosecond regime. We directly resolve in real time the strong-field driven dynamics, including Rabi-cycling as well as the competition of strong-field ionization with autoionization. The presented approach generally allows for single-shot measurements of real-time-resolved response functions for non-equilibrium states of matter. [1] V.Stooß et al., PRL accepted, September 2018

### Extraction of laser-coherent information from a photoelectron spectrum of a complex target using the phase-of-the-phase

Tulsky, Vasily

A commonly used way to obtain information about the inner structure of an atomic-scale target is the application of an intense laser to it in order to produce and analyze the spectrum of outcoming electrons. However, if a target is complex, this spectrum contains a significant (or even dominant) fraction of electrons in the total signal that is influenced by laser-incoherent scattering or is produced by thermal emission. A recently developed phase-of-the-phase (PoP) technique (see [1-6] and references therein) allows to reveal the coherent part of the signal, subtracting the rest. In order to demonstrate it we introduce a model of a spectrum obtained after application of an intense laser to an argon atom trapped inside a helium droplet. Photoelectrons produced from argon may experience multiple elastic scattering on helium atoms of the droplet before reaching the detector, and a fraction of such laser-incoherent electrons may be dominant. Nevertheless, the PoP technique can successfuly retrieve the features produced by a small remaining portion of laser-coherent electrons in the total signal. References [1] S. Skruszewicz, J. Tiggesbäumker, K.-H. Meiwes-Broer, M. Arbeiter, Th. Fennel, and D. Bauer, Phys. Rev. Lett. 115, 043001 (2015) [2] N. Eicke and M. Lein, J. of Mod. Opt., 64:10-11, 981-986 (2016) [3] M. A. Almajid, M. Zabel, S. Skruszewicz, J. Tiggesbäumker and D. Bauer, J. Phys. B 50, 19 (2017) [4] L. Seiffert, J. Köhn, C. Peltz, M. F. Kling and T. Fennel, J. Phys. B 50, 224001 (2017) [5] M. Kübel, C. Burger, R. Siemering et al, Mol. Phys. 115:15-16, 1835-1845 (2017) [6] V.A. Tulsky, M.A. Almajid, D.Bauer, https://arxiv.org/abs/1808.05167 (2018)

### Ionization and excitation with quasi sub-cycle laser pulses ​

Witzel, Bernd

We have studied short pulse laser ionization (< 7 fs, 750 nm) and excitation with polarization-gated laser pulses. The laser pulse used is composed of a circular section at the beginning and the end of the pulse and an experimentally-defined linearly polarized central part. The duration of the central part can be chosen continually with an experimental setup [1] and can be made smaller than a period of laser light. Processes taking place only in linearly polarized light are limited in time by the width of the gate. Due to quantum mechanics selection rules ($Delta$m ±1), multiphoton excitation of Rydberg states with high angular momentum are only possible with linearly polarized light. We show that polarization gating allows us to study excitation and ionization with quasi sub-cycle laser pulses. The method allows us to determine the shortest temporal window needed for the excitation processes. [1] C. Marceau, G. Gingras and B. Witzel, Optics Express 19(2011)3576

### Fragmentation of HeH$^+$ by intense ultrashort laser pulses

Wustelt, Philipp

The helium hydride molecular ion, HeH$^+$, is the simplest heteronuclear polar molecule and serves as a benchmark system for the investigation of multi-electron molecules and molecules with a permanent dipole. We specifically address the question: How does the permanent dipole of HeH$^+$ affect the fragmentation dynamics in intense ultrashort laser pulses? We study the laser induced laser-induced fragmentation; including non-ionizing dissociation, single ionization and double ionization; of an ion beam of helium hydride and an isotopologue at various wavelengths and intensities. These results are interpreted using reduced dimensionality solutions of the time-dependent Schr\"o dinger equation and with simulations based on Dressed surface hopping."